An oil tanker travels at a constant speed ( S meters per hour ), on a calm ocean, along a straight path. The shape of the tanker is a rectangle - W meters wide and L meters long capped by two semicircles at the bow and stern.

A patrol boat "circles" the tanker looking for any oil leaks. The patrol boat goes up the port side, across the bow, down the starboard side, and across the stern, and keeps cycling like this over and over. Relative to the ocean, the path of the patrol boat is always parallel to or perpendicular to the path of the tanker. During a cycle, the patrol boat makes four and only four turns. The speed of the patrol boat is twice the speed of the tanker.

Compared to the tanker, consider the patrol boat as a point; that its turns are instantaneous; and for safety it must maintain, at a minimum, C meters between itself and the tanker.

What is the shortest amount of time for the patrol boat to complete one cycle around the tanker in terms of C, L, S, and W?

(In reply to re: solution by Harry)

Harry wrote:
"....showing that it is describing an isosceles trapezium relative to the tanker.."

That point of view was was not specifically raised at review but I personally had that thought in mind.  However there is one very crucial point that I think you may have overlooked:
"Relative to the ocean, the path of the patrol boat is always parallel to or perpendicular to the path of the tanker."   With that point in mind the patrol boat will in fact travel a course of a parallelogram.

Posted by brianjn on 2009-10-24 00:39:20